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Polarization of thermal bremsstrahlung emission due to electron pressure anisotropy

Astrophysical plasmas are typically magnetized, with the Larmor radii of the charged particles many orders of magnitude smaller than their collisional mean free paths. The fundamental properties of such plasmas, e.g., conduction and viscosity, may depend on the instabilities driven by the anisotropy of the particle distribution functions and operating at scales comparable to the Larmor scales. We discuss a possibility that the pressure anisotropy of thermal electrons could produce polarization of thermal bremsstrahlung emission. In particular, we consider coherent large-scale motions in galaxy clusters to estimate the level of anisotropy driven by stretching of the magnetic-field lines by plasma flow and by heat fluxes associated with thermal gradients. Our estimate of the degree of polarization is $\sim 0.1 \%$ at energies $\gtrsim kT$. While this value is too low for the forthcoming generation of X-ray polarimeters, it is potentially an important proxy for the processes taking place at extremely small scales, which are impossible to resolve spatially. The absence of the effect at the predicted level may set a lower limit on the electron collisionality in the ICM. At the same time, the small value of the effect implies that it does not preclude the use of clusters as (unpolarized) calibration sources for X-ray polarimeters at this level of accuracy.